Question

The area of a semicircle of diameter 'd' is :

• A. \(\frac{\pi d^2}{16}\)
• B. \(\frac{\pi d^2}{4}\)
• C. \(\frac{\pi d^2}{8}\)
• D. \(\frac{\pi d^2}{2}\)

Hint:

Area of a full circle in terms of diameter is \( \frac{\pi d^2}{4} \). For a semicircle, just multiply by \( \frac{1}{2} \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Area of a circle is \( \pi r^2 \). Area of a semicircle is half of the circle's area.
Step 2: Key Formula or Approach:
\[ \text{Radius } (r) = \frac{d}{2} \]
\[ \text{Area of semicircle} = \frac{1}{2} \pi r^2 \]
Step 3: Detailed Explanation:
Substitute \( r = \frac{d}{2} \) into the area formula:
\[ \text{Area} = \frac{1}{2} \pi \left(\frac{d}{2}\right)^2 \]
\[ \text{Area} = \frac{1}{2} \pi \left(\frac{d^2}{4}\right) \]
\[ \text{Area} = \frac{\pi d^2}{8} \]
Step 4: Final Answer:
The area of a semicircle with diameter 'd' is \( \frac{\pi d^2}{8} \).